Alexa Ray Joel, the singer-songwriter daughter of Billy Joel and Christie Brinkley, is ready to come out from her famous parents’ shadows. But she doesn’t want to completely leave her pedigree behind.

“I want to be me my own person and convey my own identity,” Alexa says in a cover story for Resident Magazine. “But at the same time, I don’t want to deny or not pay homage to my father’s incredible body of work.”

Alexa just produced and recorded her dad’s tune “Just the Way You Are” for a Gap ad.

“Before taking on the . . . commercial, I was reticent to touch his work,” she told the mag. “But once I started playing the chords for ‘Just the Way You Are,’ it was therapeutic — I was able not to be so hard on myself; in fact, I was proud.”

Alexa, who gave the interview in her Nolita apartment, added that Gap “came to me” with the idea. “I was very flattered; I didn’t know initially what they wanted from me and when I found out they wanted me to do one of dad’s songs, I was nervous. They ended up giving me three options . . . ‘New York State of Mind,’ ‘Piano Man’ and ‘Just the Way You Are.’ I thought, ‘I can’t do “Piano Man” because I’d be piano girl’ . . . ‘New York State of Mind’ is masculine — only dad or Tony Bennett could pull it off.” In the end, “I felt passionately that I had to put my own spin on it.”

Of her love life, she reveals, “I never found my way romantically until very recently. I was very naive and I would come on too strongly . . . I didn’t know how to act around guys.”